12n
0442
(K12n
0442
)
A knot diagram
1
Linearized knot diagam
3 6 12 10 2 4 11 3 6 8 7 9
Solving Sequence
3,6
2 1
5,10
4 9 8 11 7 12
c
2
c
1
c
5
c
4
c
9
c
8
c
10
c
7
c
12
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h191026393u
16
− 1652039068u
15
+ ··· + 64719689b + 1958494945,
− 1223765713u
16
+ 10597268099u
15
+ ··· + 1553272536a − 9878621497,
u
17
− 11u
16
+ ··· + 25u − 24i
I
u
2
= h−u
9
− 5u
8
− 6u
7
+ 8u
6
+ 25u
5
+ 16u
4
− 11u
3
− 14u
2
+ b + u + 7,
− 7u
9
− 51u
8
− 149u
7
− 213u
6
− 119u
5
+ 61u
4
+ 107u
3
+ 8u
2
+ 5a − 56u − 27,
u
10
+ 8u
9
+ 27u
8
+ 49u
7
+ 47u
6
+ 12u
5
− 21u
4
− 19u
3
+ 3u
2
+ 11u + 5i
I
u
3
= h−u
8
a + 2u
8
+ ··· − a − 4, −u
8
a − u
8
+ ··· + a
2
+ 4, u
9
+ 4u
8
+ u
7
− 9u
6
+ 12u
4
+ 2u
3
+ 4u
2
+ 1i
I
u
4
= hb
4
− 2b
3
+ 3b
2
− 2b + 3, a + 1, u − 1i
I
u
5
= hb
2
+ b + 1, a − 1, u − 1i
* 5 irreducible components of dim
C
= 0, with total 51 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h1.91 × 10
8
u
16
− 1.65 × 10
9
u
15
+ · · · + 6.47 × 10
7
b + 1.96 × 10
9
, −1.22 ×
10
9
u
16
+1.06×10
10
u
15
+· · ·+1.55×10
9
a−9.88×10
9
, u
17
−11u
16
+· · ·+25u−24i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
10
=
0.787863u
16
− 6.82254u
15
+ ··· − 4.19484u + 6.35988
−2.95160u
16
+ 25.5261u
15
+ ··· + 20.2471u − 30.2612
a
4
=
−0.502780u
16
+ 4.36822u
15
+ ··· + 2.45724u − 4.87506
1.68304u
16
− 14.9279u
15
+ ··· − 10.7408u + 18.8611
a
9
=
0.787863u
16
− 6.82254u
15
+ ··· − 4.19484u + 6.35988
1.37093u
16
− 11.8653u
15
+ ··· − 6.94294u + 13.9936
a
8
=
−0.583066u
16
+ 5.04279u
15
+ ··· + 2.74810u − 7.63370
1.37093u
16
− 11.8653u
15
+ ··· − 6.94294u + 13.9936
a
11
=
−0.149136u
16
+ 1.25050u
15
+ ··· + 3.19107u − 2.49878
−0.717661u
16
+ 6.21375u
15
+ ··· + 5.68076u − 7.77323
a
7
=
−0.785878u
16
+ 6.96162u
15
+ ··· + 3.90013u − 8.90611
−0.0529908u
16
+ 0.408128u
15
+ ··· + 0.448137u − 0.173332
a
12
=
0.659584u
16
− 5.85549u
15
+ ··· − 6.23720u + 8.19166
1.16236u
16
− 10.2237u
15
+ ··· − 7.69444u + 12.0667
(ii) Obstruction class = −1
(iii) Cusp Shapes =
258679440
64719689
u
16
−
2255352174
64719689
u
15
+ ··· −
1298645313
64719689
u +
2660816310
64719689
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 33u
16
+ ··· − 5039u + 576
c
2
, c
5
u
17
+ 11u
16
+ ··· + 25u + 24
c
3
, c
6
u
17
− u
16
+ ··· + 4u + 1
c
4
, c
8
u
17
+ 14u
15
+ ··· − 6u
2
+ 1
c
7
, c
10
, c
11
u
17
− 6u
16
+ ··· + 19u − 2
c
9
, c
12
u
17
+ u
16
+ ··· + 33u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 117y
16
+ ··· + 20649889y −331776
c
2
, c
5
y
17
− 33y
16
+ ··· − 5039y −576
c
3
, c
6
y
17
+ 13y
16
+ ··· − 22y −1
c
4
, c
8
y
17
+ 28y
16
+ ··· + 12y −1
c
7
, c
10
, c
11
y
17
+ 14y
16
+ ··· + 93y −4
c
9
, c
12
y
17
+ 35y
16
+ ··· + 1875y −9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.942057 + 0.494267I
a = −0.753350 − 0.421156I
b = 0.435867 − 0.555452I
1.96186 + 2.24541I 1.44074 − 2.23530I
u = −0.942057 − 0.494267I
a = −0.753350 + 0.421156I
b = 0.435867 + 0.555452I
1.96186 − 2.24541I 1.44074 + 2.23530I
u = 1.095620 + 0.300147I
a = 0.131673 − 0.311290I
b = −1.033950 − 0.750497I
2.79366 + 0.08444I −4.63288 + 0.68709I
u = 1.095620 − 0.300147I
a = 0.131673 + 0.311290I
b = −1.033950 + 0.750497I
2.79366 − 0.08444I −4.63288 − 0.68709I
u = 0.836685
a = −0.0818231
b = 0.476471
−1.37068 −8.35980
u = −0.320479 + 0.572318I
a = 0.08297 + 1.68332I
b = −0.103629 + 0.996127I
7.44498 + 0.11919I 3.63980 − 1.93920I
u = −0.320479 − 0.572318I
a = 0.08297 − 1.68332I
b = −0.103629 − 0.996127I
7.44498 − 0.11919I 3.63980 + 1.93920I
u = −1.25347 + 0.91415I
a = 0.916560 − 0.265291I
b = 0.46012 + 1.98973I
5.01538 + 5.62718I −1.75252 − 3.01899I
u = −1.25347 − 0.91415I
a = 0.916560 + 0.265291I
b = 0.46012 − 1.98973I
5.01538 − 5.62718I −1.75252 + 3.01899I
u = −0.032060 + 0.412278I
a = −1.57998 − 0.21566I
b = −0.592975 + 0.413733I
0.026615 − 1.286250I 0.68462 + 4.17584I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.032060 − 0.412278I
a = −1.57998 + 0.21566I
b = −0.592975 − 0.413733I
0.026615 + 1.286250I 0.68462 − 4.17584I
u = 2.13442 + 0.33433I
a = −0.041538 + 1.111040I
b = 1.96060 − 2.85602I
−10.20570 − 0.23808I −2.00230 − 0.80635I
u = 2.13442 − 0.33433I
a = −0.041538 − 1.111040I
b = 1.96060 + 2.85602I
−10.20570 + 0.23808I −2.00230 + 0.80635I
u = 2.15252 + 0.26857I
a = 0.260975 − 1.202630I
b = −2.33574 + 2.94126I
−7.3294 − 12.2045I −2.87951 + 5.29191I
u = 2.15252 − 0.26857I
a = 0.260975 + 1.202630I
b = −2.33574 − 2.94126I
−7.3294 + 12.2045I −2.87951 − 5.29191I
u = 2.24717 + 0.01207I
a = −0.122236 + 1.201380I
b = 0.47148 − 3.89441I
−13.0039 − 6.5145I −5.31806 + 4.17343I
u = 2.24717 − 0.01207I
a = −0.122236 − 1.201380I
b = 0.47148 + 3.89441I
−13.0039 + 6.5145I −5.31806 − 4.17343I
6
II.
I
u
2
= h−u
9
−5u
8
+· · ·+b+7, −7u
9
−51u
8
+· · ·+5a−27, u
10
+8u
9
+· · ·+11u+5i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
10
=
7
5
u
9
+
51
5
u
8
+ ··· +
56
5
u +
27
5
u
9
+ 5u
8
+ 6u
7
− 8u
6
− 25u
5
− 16u
4
+ 11u
3
+ 14u
2
− u − 7
a
4
=
4
5
u
9
+
27
5
u
8
+ ··· +
32
5
u +
9
5
−u
9
− 8u
8
− 26u
7
− 43u
6
− 33u
5
+ 3u
4
+ 24u
3
+ 10u
2
− 9u − 9
a
9
=
7
5
u
9
+
51
5
u
8
+ ··· +
56
5
u +
27
5
u
9
+ 6u
8
+ 13u
7
+ 10u
6
− 5u
5
− 12u
4
− u
3
+ 7u
2
+ 3u − 2
a
8
=
2
5
u
9
+
21
5
u
8
+ ··· +
41
5
u +
37
5
u
9
+ 6u
8
+ 13u
7
+ 10u
6
− 5u
5
− 12u
4
− u
3
+ 7u
2
+ 3u − 2
a
11
=
13
5
u
9
+
89
5
u
8
+ ··· +
84
5
u +
23
5
−u
9
− 9u
8
− 33u
7
− 61u
6
− 52u
5
+ 2u
4
+ 38u
3
+ 16u
2
− 15u − 13
a
7
=
−
9
5
u
9
−
67
5
u
8
+ ··· −
77
5
u −
54
5
−2u
9
− 13u
8
− 33u
7
− 39u
6
− 12u
5
+ 21u
4
+ 18u
3
− 4u
2
− 11u − 1
a
12
=
1
5
u
9
+
8
5
u
8
+ ··· +
8
5
u +
16
5
u
9
+ 7u
8
+ 20u
7
+ 29u
6
+ 18u
5
− 6u
4
− 15u
3
− 4u
2
+ 7u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −8u
9
− 57u
8
− 163u
7
− 230u
6
− 130u
5
+ 61u
4
+ 115u
3
+ 15u
2
− 61u − 34
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− 10u
9
+ ··· − 91u + 25
c
2
u
10
+ 8u
9
+ ··· + 11u + 5
c
3
, c
6
u
10
+ u
9
+ 3u
8
+ u
6
− 3u
5
− 2u
4
− u
3
+ 2u + 1
c
4
, c
8
u
10
+ 6u
8
+ 7u
6
− 2u
5
+ 5u
4
+ 2u
3
+ 5u
2
+ 2u + 1
c
5
u
10
− 8u
9
+ ··· − 11u + 5
c
7
u
10
− 3u
9
+ ··· − 10u + 3
c
9
, c
12
u
10
− u
9
+ 6u
8
− 10u
7
+ 10u
6
− 6u
5
+ 2u
4
− u
3
+ 2u
2
− u + 1
c
10
, c
11
u
10
+ 3u
9
+ ··· + 10u + 3
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
− 22y
9
+ ··· + 2569y + 625
c
2
, c
5
y
10
− 10y
9
+ ··· − 91y + 25
c
3
, c
6
y
10
+ 5y
9
+ 11y
8
+ 8y
7
− 9y
6
− 15y
5
+ 4y
4
+ 13y
3
− 4y + 1
c
4
, c
8
y
10
+ 12y
9
+ ··· + 6y + 1
c
7
, c
10
, c
11
y
10
+ 9y
9
+ ··· + 20y + 9
c
9
, c
12
y
10
+ 11y
9
+ 36y
8
+ 12y
7
+ 6y
6
+ 8y
5
+ 24y
4
+ 15y
3
+ 6y
2
+ 3y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.698244 + 0.611679I
a = −0.594983 + 0.452728I
b = −1.12357 − 1.18282I
6.61177 + 7.24611I 1.48024 − 6.55546I
u = −0.698244 − 0.611679I
a = −0.594983 − 0.452728I
b = −1.12357 + 1.18282I
6.61177 − 7.24611I 1.48024 + 6.55546I
u = −0.765895 + 0.862612I
a = 0.577252 + 0.100829I
b = 0.25692 + 1.47319I
1.12408 + 3.31101I −1.94210 − 5.90631I
u = −0.765895 − 0.862612I
a = 0.577252 − 0.100829I
b = 0.25692 − 1.47319I
1.12408 − 3.31101I −1.94210 + 5.90631I
u = 0.649524 + 0.270637I
a = 0.986717 + 0.863844I
b = 0.280240 − 0.198619I
−0.88058 + 1.43796I −7.95798 − 4.23415I
u = 0.649524 − 0.270637I
a = 0.986717 − 0.863844I
b = 0.280240 + 0.198619I
−0.88058 − 1.43796I −7.95798 + 4.23415I
u = −1.11228 + 0.88745I
a = −0.346880 − 0.585052I
b = 1.56427 − 1.47362I
5.04002 − 1.56785I −0.680979 + 1.239329I
u = −1.11228 − 0.88745I
a = −0.346880 + 0.585052I
b = 1.56427 + 1.47362I
5.04002 + 1.56785I −0.680979 − 1.239329I
u = −2.07310 + 0.22780I
a = 0.077895 + 1.141750I
b = −1.47786 − 2.59954I
−11.89530 + 1.62532I −4.89918 − 0.65986I
u = −2.07310 − 0.22780I
a = 0.077895 − 1.141750I
b = −1.47786 + 2.59954I
−11.89530 − 1.62532I −4.89918 + 0.65986I
10
III. I
u
3
= h−u
8
a + 2u
8
+ · · · − a − 4, −u
8
a − u
8
+ · · · + a
2
+ 4, u
9
+ 4u
8
+
u
7
− 9u
6
+ 12u
4
+ 2u
3
+ 4u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
10
=
a
1
8
u
8
a −
1
4
u
8
+ ··· +
1
8
a +
1
2
a
4
=
−
1
4
u
8
a +
7
8
u
8
+ ··· +
1
2
a +
15
8
1
4
u
8
a +
3
8
u
8
+ ··· +
1
2
a −
5
8
a
9
=
a
1
8
u
8
a −
1
4
u
8
+ ··· +
1
8
a +
1
2
a
8
=
−
1
8
u
8
a +
1
4
u
8
+ ··· +
7
8
a −
1
2
1
8
u
8
a −
1
4
u
8
+ ··· +
1
8
a +
1
2
a
11
=
−
1
4
u
8
a +
1
2
u
8
+ ··· +
1
2
a +
5
4
1
8
u
8
a −
3
4
u
8
+ ··· +
3
8
a −
3
4
a
7
=
−
1
2
u
8
a −
7
8
u
8
+ ··· −
1
4
a −
7
8
1
4
u
8
a +
3
8
u
8
+ ··· +
3
4
a −
3
8
a
12
=
−u
8
− 4u
7
− u
6
+ 9u
5
− 12u
3
− 2u
2
− 4u
1
2
u
8
a +
1
8
u
8
+ ··· +
1
4
a −
7
8
(ii) Obstruction class = −1
(iii) Cusp Shapes =
5
4
u
8
+
25
4
u
7
+
7
2
u
6
−
63
4
u
5
−
15
4
u
4
+
93
4
u
3
+
7
4
u
2
+
27
4
u −
13
4
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 14u
8
+ 73u
7
+ 173u
6
+ 188u
5
+ 80u
4
− 74u
3
+ 40u
2
− 8u + 1)
2
c
2
, c
5
(u
9
− 4u
8
+ u
7
+ 9u
6
− 12u
4
+ 2u
3
− 4u
2
− 1)
2
c
3
, c
6
u
18
− 4u
17
+ ··· − 19u + 7
c
4
, c
8
u
18
+ 17u
16
+ ··· − 33u + 61
c
7
, c
10
, c
11
(u
9
+ u
8
+ 5u
7
+ 4u
6
+ 8u
5
+ 5u
4
+ 3u
3
− 2u − 2)
2
c
9
, c
12
u
18
− 3u
17
+ ··· − 38u + 787
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
9
− 50y
8
+ ··· − 16y −1)
2
c
2
, c
5
(y
9
− 14y
8
+ 73y
7
− 173y
6
+ 188y
5
− 80y
4
− 74y
3
− 40y
2
− 8y −1)
2
c
3
, c
6
y
18
+ 2y
17
+ ··· + 451y + 49
c
4
, c
8
y
18
+ 34y
17
+ ··· + 4279y + 3721
c
7
, c
10
, c
11
(y
9
+ 9y
8
+ 33y
7
+ 60y
6
+ 50y
5
+ 7y
4
− 7y
3
+ 8y
2
+ 4y −4)
2
c
9
, c
12
y
18
+ 29y
17
+ ··· + 1731530y + 619369
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.149930 + 0.591217I
a = −0.601255 − 0.402054I
b = −0.395481 + 0.118419I
1.86176 + 1.02570I −2.63382 − 1.45009I
u = 1.149930 + 0.591217I
a = 1.283380 − 0.095795I
b = −0.77918 − 2.34414I
1.86176 + 1.02570I −2.63382 − 1.45009I
u = 1.149930 − 0.591217I
a = −0.601255 + 0.402054I
b = −0.395481 − 0.118419I
1.86176 − 1.02570I −2.63382 + 1.45009I
u = 1.149930 − 0.591217I
a = 1.283380 + 0.095795I
b = −0.77918 + 2.34414I
1.86176 − 1.02570I −2.63382 + 1.45009I
u = −0.256958 + 0.481474I
a = 2.09172 + 0.18082I
b = −0.347105 + 0.467672I
5.86635 − 5.34937I −0.84423 + 2.78056I
u = −0.256958 + 0.481474I
a = 0.39890 − 2.37095I
b = 1.48260 − 1.54705I
5.86635 − 5.34937I −0.84423 + 2.78056I
u = −0.256958 − 0.481474I
a = 2.09172 − 0.18082I
b = −0.347105 − 0.467672I
5.86635 + 5.34937I −0.84423 − 2.78056I
u = −0.256958 − 0.481474I
a = 0.39890 + 2.37095I
b = 1.48260 + 1.54705I
5.86635 + 5.34937I −0.84423 − 2.78056I
u = 0.202323 + 0.429977I
a = −1.06958 − 1.32915I
b = −0.028684 + 0.501202I
−0.08117 − 1.83340I −4.79553 + 3.05314I
u = 0.202323 + 0.429977I
a = −1.78447 + 1.20971I
b = −0.54712 + 1.46919I
−0.08117 − 1.83340I −4.79553 + 3.05314I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.202323 − 0.429977I
a = −1.06958 + 1.32915I
b = −0.028684 − 0.501202I
−0.08117 + 1.83340I −4.79553 − 3.05314I
u = 0.202323 − 0.429977I
a = −1.78447 − 1.20971I
b = −0.54712 − 1.46919I
−0.08117 + 1.83340I −4.79553 − 3.05314I
u = −2.04009 + 0.22792I
a = −0.374086 − 0.921422I
b = 2.26253 + 1.38756I
−10.25890 + 3.35426I −1.96692 − 2.76177I
u = −2.04009 + 0.22792I
a = −0.189467 + 1.360530I
b = −0.72311 − 3.40708I
−10.25890 + 3.35426I −1.96692 − 2.76177I
u = −2.04009 − 0.22792I
a = −0.374086 + 0.921422I
b = 2.26253 − 1.38756I
−10.25890 − 3.35426I −1.96692 + 2.76177I
u = −2.04009 − 0.22792I
a = −0.189467 − 1.360530I
b = −0.72311 + 3.40708I
−10.25890 − 3.35426I −1.96692 + 2.76177I
u = −2.11041
a = 0.244866 + 1.162790I
b = −0.92445 − 2.96892I
−14.5153 −7.51900
u = −2.11041
a = 0.244866 − 1.162790I
b = −0.92445 + 2.96892I
−14.5153 −7.51900
15
IV. I
u
4
= hb
4
− 2b
3
+ 3b
2
− 2b + 3, a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
5
=
1
0
a
10
=
−1
b
a
4
=
−b + 1
b
2
a
9
=
−1
b − 1
a
8
=
−b
b − 1
a
11
=
−b
3
+ b
2
− b − 1
b
3
− 2b
2
+ 3b − 1
a
7
=
−b
2
+ 2b − 1
b
3
− b
2
+ 1
a
12
=
1
−b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
6
u
4
+ 2u
3
+ 3u
2
+ 2u + 3
c
4
, c
8
u
4
− 2u
3
+ 3u
2
− 2u + 3
c
5
, c
9
, c
12
(u + 1)
4
c
7
, c
10
, c
11
(u
2
+ 2)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
9
, c
12
(y −1)
4
c
3
, c
4
, c
6
c
8
y
4
+ 2y
3
+ 7y
2
+ 14y + 9
c
7
, c
10
, c
11
(y + 2)
4
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −0.152220 + 1.084150I
4.93480 0
u = 1.00000
a = −1.00000
b = −0.152220 − 1.084150I
4.93480 0
u = 1.00000
a = −1.00000
b = 1.15222 + 1.08415I
4.93480 0
u = 1.00000
a = −1.00000
b = 1.15222 − 1.08415I
4.93480 0
19
V. I
u
5
= hb
2
+ b + 1, a − 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
5
=
1
0
a
10
=
1
b
a
4
=
b + 1
−b − 1
a
9
=
1
b + 1
a
8
=
−b
b + 1
a
11
=
1
b
a
7
=
−b
b + 1
a
12
=
1
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
9
c
12
(u − 1)
2
c
3
, c
4
, c
6
c
8
u
2
+ u + 1
c
5
(u + 1)
2
c
7
, c
10
, c
11
u
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
9
, c
12
(y −1)
2
c
3
, c
4
, c
6
c
8
y
2
+ y + 1
c
7
, c
10
, c
11
y
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = −0.500000 + 0.866025I
0 −6.00000
u = 1.00000
a = 1.00000
b = −0.500000 − 0.866025I
0 −6.00000
23
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
· (u
9
+ 14u
8
+ 73u
7
+ 173u
6
+ 188u
5
+ 80u
4
− 74u
3
+ 40u
2
− 8u + 1)
2
· (u
10
− 10u
9
+ ··· − 91u + 25)(u
17
+ 33u
16
+ ··· − 5039u + 576)
c
2
(u − 1)
6
(u
9
− 4u
8
+ u
7
+ 9u
6
− 12u
4
+ 2u
3
− 4u
2
− 1)
2
· (u
10
+ 8u
9
+ ··· + 11u + 5)(u
17
+ 11u
16
+ ··· + 25u + 24)
c
3
, c
6
(u
2
+ u + 1)(u
4
+ 2u
3
+ 3u
2
+ 2u + 3)
· (u
10
+ u
9
+ ··· + 2u + 1)(u
17
− u
16
+ ··· + 4u + 1)
· (u
18
− 4u
17
+ ··· − 19u + 7)
c
4
, c
8
(u
2
+ u + 1)(u
4
− 2u
3
+ 3u
2
− 2u + 3)
· (u
10
+ 6u
8
+ 7u
6
− 2u
5
+ 5u
4
+ 2u
3
+ 5u
2
+ 2u + 1)
· (u
17
+ 14u
15
+ ··· − 6u
2
+ 1)(u
18
+ 17u
16
+ ··· − 33u + 61)
c
5
(u + 1)
6
(u
9
− 4u
8
+ u
7
+ 9u
6
− 12u
4
+ 2u
3
− 4u
2
− 1)
2
· (u
10
− 8u
9
+ ··· − 11u + 5)(u
17
+ 11u
16
+ ··· + 25u + 24)
c
7
u
2
(u
2
+ 2)
2
(u
9
+ u
8
+ 5u
7
+ 4u
6
+ 8u
5
+ 5u
4
+ 3u
3
− 2u − 2)
2
· (u
10
− 3u
9
+ ··· − 10u + 3)(u
17
− 6u
16
+ ··· + 19u − 2)
c
9
, c
12
(u − 1)
2
(u + 1)
4
· (u
10
− u
9
+ 6u
8
− 10u
7
+ 10u
6
− 6u
5
+ 2u
4
− u
3
+ 2u
2
− u + 1)
· (u
17
+ u
16
+ ··· + 33u + 3)(u
18
− 3u
17
+ ··· − 38u + 787)
c
10
, c
11
u
2
(u
2
+ 2)
2
(u
9
+ u
8
+ 5u
7
+ 4u
6
+ 8u
5
+ 5u
4
+ 3u
3
− 2u − 2)
2
· (u
10
+ 3u
9
+ ··· + 10u + 3)(u
17
− 6u
16
+ ··· + 19u − 2)
24
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
9
− 50y
8
+ ··· − 16y −1)
2
· (y
10
− 22y
9
+ ··· + 2569y + 625)
· (y
17
− 117y
16
+ ··· + 20649889y −331776)
c
2
, c
5
(y −1)
6
· (y
9
− 14y
8
+ 73y
7
− 173y
6
+ 188y
5
− 80y
4
− 74y
3
− 40y
2
− 8y −1)
2
· (y
10
− 10y
9
+ ··· − 91y + 25)(y
17
− 33y
16
+ ··· − 5039y −576)
c
3
, c
6
(y
2
+ y + 1)(y
4
+ 2y
3
+ 7y
2
+ 14y + 9)
· (y
10
+ 5y
9
+ 11y
8
+ 8y
7
− 9y
6
− 15y
5
+ 4y
4
+ 13y
3
− 4y + 1)
· (y
17
+ 13y
16
+ ··· − 22y −1)(y
18
+ 2y
17
+ ··· + 451y + 49)
c
4
, c
8
(y
2
+ y + 1)(y
4
+ 2y
3
+ ··· + 14y + 9)(y
10
+ 12y
9
+ ··· + 6y + 1)
· (y
17
+ 28y
16
+ ··· + 12y −1)(y
18
+ 34y
17
+ ··· + 4279y + 3721)
c
7
, c
10
, c
11
y
2
(y + 2)
4
· (y
9
+ 9y
8
+ 33y
7
+ 60y
6
+ 50y
5
+ 7y
4
− 7y
3
+ 8y
2
+ 4y −4)
2
· (y
10
+ 9y
9
+ ··· + 20y + 9)(y
17
+ 14y
16
+ ··· + 93y −4)
c
9
, c
12
(y −1)
6
· (y
10
+ 11y
9
+ 36y
8
+ 12y
7
+ 6y
6
+ 8y
5
+ 24y
4
+ 15y
3
+ 6y
2
+ 3y + 1)
· (y
17
+ 35y
16
+ ··· + 1875y −9)
· (y
18
+ 29y
17
+ ··· + 1731530y + 619369)
25
